Case Study: Specialty Toys

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Register to read the introduction… If inventory remains after the holiday season, Specialty will sell all surplus inventories for $5 per unit. After reviewing the sales history of similar products, Specialty’s senior forecaster predicted an expected demand of 20,000 units with a .95 probability that demand would be between 10,000 units and 30,000 units. 1. Use the sales forecaster’s prediction to describe a normal probability distribution that can be used to approximate the demand distribution. Sketch the distribution and show its mean and standard deviation. 2. compute the probability of a stock-out for the order quantities suggested by members of the management team 3. compute the projected profit for the order quantities suggested by the management team under three scenarios: worst case in wwhich sales = 10000 units, most likely case in which sales=20000 units and best case in which sales=30000 units 4. one of specialty's managerrs felt that the profit potential was so great that the order quantity should have a 70% chance of meeting demand and only a 30%chance of any stock-outs. what quantity would be ordered under this policy and what is the projected profit under the three sales …show more content…
Then X follows normal distribution with mean μ = 20000 and standard deviation σ. Then P(10000 < X < 30000) = 0.95
P((10000-20000)/σ < (X-20000)/σ < (30000-20000)/σ) = 0.95
From tables of areas under the standard normal curve (30000-20000)/σ = 1.96 σ = (30000-20000)/1.96 =10000/1.96 = 5102 1. The demand distribution can be approximated by a normal distribution with mean µ = 20000 and standard deviation σ = 5102.

2. Probability of stock out with an order of K units is P(X > K) = P(Z > (K-20000)/5102), where Z is distributed as standard normal Order (K) | (K-20000)/5102 | P(X > K) | 15000 | -0.98001 | 0.836458876 | 18000 | -0.392 | 0.652472052 | 24000 | 0.784006 | 0.216518215 | 28000 | 1.568013 | 0.058439102 |

3. The projected profit for the different order quantities and scenarios are given in the following table.

Order | Scenario 10000 | Scenario 20000 | Scenario 30000 | 15000 | 8*10000-11*5000 =25000 | 8*15000=120000 | 8*15000 = 120000 | 18000 | 8*10000-11*8000= -8000 | 8*18000 = 144000 | 8*18000 = 144000 | 24000 | 8*10000-11*14000= -74000 | 8*20000-11*4000=116000 | 8*24000 = 192000 | 28000 | 8*10000-11*18000= -118000 | 8*2000-11*8000=72000 | 8*28000 = 224000

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